Abstract: Virtual integration in moduli problems: We will discuss a method of carrying out integration on moduli spaces defined from Fredholm systems. The main point is that we do away with the regularity assumptions that is generally used in such a setup to obtain smooth manifolds (or orbifolds). We will also discuss some applications for such an integration. Most of the constructions will be elementary and will be motivated from finite dimensional examples. This is based on works of Chen-Li-Tian and works in progress with Chen and Hyvrier.